Methods for exact solutions of nonlinear ordinary differential equations\

In order to find closed form solutions of nonintegrable nonlinear ordinary differential equations, numerous tricks have been proposed. The goal of this short review is to recall classical, 19th-century results, completed in 2006 by Eremenko, which can be turned into algorithms, thus avoiding ad hoc assumptions, able to provide all (as opposed to some) solutions in a precise class. To illustrate these methods, we present some new such exact solutions, physically relevent.